Question: The following line passes through point $(-3, 9)$ : $y = -\dfrac{15}{11} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-3, 9)$ into the equation gives: $9 = -\dfrac{15}{11} \cdot -3 + b$ $9 = \dfrac{45}{11} + b$ $b = 9 - \dfrac{45}{11}$ $b = \dfrac{54}{11}$ Plugging in $\dfrac{54}{11}$ for $b$, we get $y = -\dfrac{15}{11} x + \dfrac{54}{11}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-3, 9)$